Temporal Scaling of Interfaces Propagating in Porous Media

TL;DR

This study investigates the temporal roughening behavior of a wetting front in porous media, revealing a force-independent scaling law and suggesting non-linear dynamics due to anisotropic depinning.

Contribution

First experimental evidence of force-independent temporal scaling in a propagating wetting front with quenched noise, highlighting non-linear effects.

Findings

Measured autocorrelation function shows power-law behavior with exponent 0.56

Temporal scaling is independent of driving force

Results suggest non-linear dynamics due to anisotropic depinning

Abstract

To better understand the temporal behavior of a roughening meniscus driven by capillary forces during the imbibition of a viscous fluid in porous media, we measure the height-height autocorrelation function $C(t)$ using a constant driving force. We find $C(t)\sim t^{\beta}$, with $\beta = 0.56\pm 0.03$, and provide the first experimental evidence for driving force independent temporal scaling behavior of a propagating wetting front in the presence of quenched noise. We interpret the value of ${\beta}$ in terms of the possibility that the dynamics may be governed by nonvanishing non-linearity due to anisotropic depinning.